Problem: What number could replace $a$ below? $\dfrac{1}{3} = \dfrac{3}{a}$
Explanation: The fraction on the left represents 1 out of 3 slices of a rectangular pie. How many total slices would we need if we want the same amount of pie in 3 slices? We would need to cut the pie into 9 slices. $\dfrac{1}{3} = \dfrac{3}{9}$ and so the answer is $9$ Another way to get the answer is to multiply by $\dfrac{3}{3}$ $\dfrac{3}{3} = \dfrac{1}{1} = 1$ so really we are multiplying by 1. The final equation is: $\dfrac{1}{3} \times \dfrac{3}{3} = \dfrac{3}{9} $ so our answer is $9$.